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Quasi-modes and resonances in two-dimensional vortices with radial stratification

   Department of Mathematics

   Friday, July 22, 2022  Competition Funded PhD Project (UK Students Only)

About the Project

This project examines both the linear and nonlinear evolution of a two-dimensional axisymmetric vortex with a radial density stratification. These vortices will be perturbed by axisymmetric vorticity perturbations, and by using linear stability analysis we can examine the existence of a critical layer within such vortices. In particular we are interested in critical layer positions which give a resonant response for the perturbation. These linear calculations will be supplemented by nonlinear simulations of the system under various forcing scenarios in order to identify when nonlinear structures persist for large times, or when the vortex returns to an axisymmetric state.

The successful candidate will receive comprehensive research training related to all aspects of the research and opportunities to participate in conferences, workshops and seminars to develop professional skills and research network.

Supervisor: Dr Matthew Turner

This is a minimum 3 year project. We are able to offer this opportunity starting in October 2022.

Entry requirements

Applicants should have a minimum of a first class honours degree in mathematics, the physical sciences or engineering. Preferably applicants will hold a MMath, MPhys or MSc degree, though exceptional BSc students will be considered.

English language requirements: IELTS Academic 6.5 or above (or equivalent) with 6.0 in each individual category.

How to apply

Applications should be submitted via the Mathematics PhD programme page on the "Apply" tab.

Please state clearly the studentship project at you would like to apply for.

Funding Notes

Full UK tuition fees and a tax-free stipend. This project is on offer in competition with a number of other projects for funding. This opportunity may be available with partial funding for overseas fees for exceptional applicants. However, funding for overseas students is limited and applicants are encouraged to find suitable funding themselves. Funded by the University of Surrey.


Dixit, H. N. and Govindarajan, R. (2011) Stability of a vortex in radial density stratification: role of wave interactions. J. Fluid Mech. 679 582-615.

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